Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.

Presents an introduction to the origins and principles of geometry, describing geometric constructions that can be achieved through the use of rulers and compasses.

Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.

Topics include: Segment Constructions; Angles Constructions; Constructions Based on Congruent Triangle Theorems; Special Segments in Triangles; Circle Constructions.

"'Geometry by construction' challenges its readers to participate in the creation of mathematics. The questions span the spectrum from easy to newly published research and so are appropriate for a variety of students and teachers. From differentiation in a high school course through college classes and into summer research, any interested geometer will find compelling material"--Back cover.

Practical Handbook of Spreadsheet Curves and Geometric Constructions presents a compelling description of how to use commercially available spreadsheets to design and create high-quality graphs of a variety of curves, including classical curves in mathematics. The book contains more than 65 models for the geometric construction of families of curves such as strophoids, pedals, involutes, and others. Models in the book are designed to be interactive so that users can experiment with them to produce eye-catching curves, designs, and patterns. Examples come from calculus, parametric equations, constructions of classical families, and graphs of conformal mappings of a complex variable. The author, a leading authority on spreadsheets, presents innovative techniques for using spreadsheet graphing to generate large families of lines and circles that describe various curves as envelopes of the families. The final chapter of the book discusses the use of commercial spreadsheets to create animation effects. The book is heavily illustrated, with more than 200 graphs and 60 tables. An accompanying 3.5" disk provides 25 selected examples written in Quattro Pro 2.0, Lotus 1-2-3 2.3, and Microsoft Excel 4.0. Designed for both experienced and novice spreadsheet users, Practical Handbook of Spreadsheet Curves and Geometric Constructions will be an invaluable resource for mathematicians, engineers, scientists, and computer scientists. The book will also benefit professional artists and designers interested in learning new techniques for producing mathematical curves using spreadsheet software.

The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus. Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise. The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.